There are currently 26 operands for parameters or variables. They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. For equations may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

to:

The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. For equations may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

There are currently 21 operands for parameters or variables. They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.

to:

There are currently 26 operands for parameters or variables. They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''. For equations may be in the form of equalities (=) or inequalities (>,<). For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.

A couple differential and algebraic equations are shown below. The steady-state solution is p=2, x=-1.0445, y=0.1238, and z=-1.0445. For steady-state solutions the differential variables (''$x'') are set to zero. Variables x, y, and z were not given initial values. In the absence of an initial condition, variables are set to a default value of 1.0.

to:

A couple differential and algebraic equations are shown below. For steady-state solutions the differential variables (''$x'') are set to zero. Variables x, y, and z were not given initial values. In the absence of an initial condition, variables are set to a default value of 1.0.

A couple differential and algebraic equations are shown below. The steady-state solution is p=2, x=-1.0445, y=0.1238, and z=-1.0445. For steady-state solutions the differential variables (''$x'') are set to zero.

to:

A couple differential and algebraic equations are shown below. The steady-state solution is p=2, x=-1.0445, y=0.1238, and z=-1.0445. For steady-state solutions the differential variables (''$x'') are set to zero. Variables x, y, and z were not given initial values. In the absence of an initial condition, variables are set to a default value of 1.0.

A couple differential and algebraic equations are shown below. The steady-state solution is p=2, x=-1.0445, y=0.1238, and z=-1.0445. For steady-state solutions the differential variables (''$x'') are set to zero.

''Open-equation format'' is allowed for differential and algebraic equations. ''Open-equation'' means that the equation can be expressed in the least restrictive form. Other software packages require differential equations to be posed in the semi-explicit form: dx/dt = f(x). This is not required with %blue%A%red%P%black%Monitor modelling language.

to:

''Open-equation format'' is allowed for differential and algebraic equations. ''Open-equation'' means that the equation can be expressed in the least restrictive form. Other software packages require differential equations to be posed in the semi-explicit form: dx/dt = f(x). This is not required with %blue%A%red%P%black%Monitor modelling language. All equations are automatically transformed into residual form.

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|| $ ||Differential || $x = -x + y

to:

|| $ ||Differential || $x = -x + y ||

!!! Equation Example

Changed line 45 from:

p = 1

to:

p = 2

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Equations ! The program tranforms all equations from the 'original form' to ! the 'residual form'. Sparse first derivatives ! of the residual are reported with respect to the variable values. x = y ! Original form x-y = 0 ! Residual form

! Differential equation with $ indicating a differential with respect to time ! Sparsity pattern is augmented by n columns where n is the number of variables ! If x is the first variable and there are 3 variables then $x would be variable 4 ! x=1 ! y=2 ! z=3 ! $x=4 ! $y=5 ! $z=6 $x = -x + y

Parameters are fixed values that represent model inputs, fixed constants, or any other value that does not change. Parameters are not modified by the solver as it searches for a solution. As such, parameters do not contribute to the number of degrees of freedom (DOF).

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Equations consist of a collection of parameters and variables that are related by operands (+,-,*,/,exp(),d()/dt, etc.).The equations define the relationship between variables.

Added lines 7-36:

''Open-equation format'' is allowed for differential and algebraic equations. ''Open-equation'' means that the equation can be expressed in the least restrictive form. Other software packages require differential equations to be posed in the semi-explicit form: dx/dt = f(x). This is not required with %blue%A%red%P%black%Monitor modelling language.

!!! Equation operands

There are currently 21 operands for parameters or variables. They are listed below with a short description of each and a simple example involving variable ''x'' and optionally ''y''.

Parameters are fixed values that represent model inputs, fixed constants, or any other value that does not change. Parameters are not modified by the solver as it searches for a solution. As such, parameters do not contribute to the number of degrees of freedom (DOF).

Equations are declared in the ''Equations ... End Equations'' section of the model file. The equations may be defined in one section or in multiple declarations throughout the model. Equations are parsed sequentially, from top to bottom. However, implicit equations are solved simultaneously so the order of the equations does not change the solution.

Equations ! The program tranforms all equations from the 'original form' to ! the 'residual form'. Sparse first derivatives ! of the residual are reported with respect to the variable values. x = y ! Original form x-y = 0 ! Residual form

! Differential equation with $ indicating a differential with respect to time ! Sparsity pattern is augmented by n columns where n is the number of variables ! If x is the first variable and there are 3 variables then $x would be variable 4 ! x=1 ! y=2 ! z=3 ! $x=4 ! $y=5 ! $z=6 $x = -x + y